Does this Paradox break Special Relativity?
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John Clark
Jul 16, 2022, 3:34:23 PM7/16/22
to 'Brent Meeker' via Everything List
Spoiler alert: The answer is no, but the resolution is subtle and the video is fun:
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Lawrence Crowell
Jul 16, 2022, 4:25:06 PM7/16/22
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Here is a quick way to see this. Consider the diagram below
These correspond to two accelerated frames that on the x and x' axes defines the simultaneous start of the two rocket ships. The dotted lines are the Rindler horizons for the two observers. The green line is the spatial interval connecting the two observers. We can see right away that at the 3rd green line connects the two observers where the right observer will witness the left observer on its Rindler horizon. This is the causal limit, where the left observer cannot send a signal to the right observer. At that point it is as if it fell into a black hole. The right observer at the point the left observer witnesses the left observer reach the horizon will calculate an interval to this left observer as infinite. At this point and beyond no possible connecting line can exist. As the green line is transformed it becomes longer and longer, and at the horizon limit there can not exist a physical connection.
These correspond to two accelerated frames that on the x and x' axes defines the simultaneous start of the two rocket ships. The dotted lines are the Rindler horizons for the two observers. The green line is the spatial interval connecting the two observers. We can see right away that at the 3rd green line connects the two observers where the right observer will witness the left observer on its Rindler horizon. This is the causal limit, where the left observer cannot send a signal to the right observer. At that point it is as if it fell into a black hole. The right observer at the point the left observer witnesses the left observer reach the horizon will calculate an interval to this left observer as infinite. At this point and beyond no possible connecting line can exist. As the green line is transformed it becomes longer and longer, and at the horizon limit there can not exist a physical connection.
LC
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